f^*-vectors of lattice polytopes (Max Hlavacek, Pomona College)
The Ehrhart polynomial of a lattice polytope P counts the number of integer points in the nth integral dilate of P. The f^* -vector of P, introduced by Felix Breuer […]
12 events found.
Algebra / Number Theory / Combinatorics Seminar
Events
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Roberts North 102, CMC
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On the Cox ring of a weighted projective plane blown-up at a point (Javier Gonzalez Anaya, HMC)
Roberts North 102, CMCThe Cox ring of a projective variety is the ring of all its meromorphic functions, together with a grading of geometric origin. Determining whether this ring is finitely generated is […]
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What can chicken nuggets tell us about symmetric functions, positive polynomials, random norms, and AF algebras? (Stephan Garcia, Pomona)
Roberts North 102, CMCA simple question about chicken nuggets connects everything from analysis and combinatorics to probability theory and computer-aided design. With tools from complex, harmonic, and functional analysis, probability theory, algebraic combinatorics, […]
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Skein algebra of a punctured surface (Helen Wong, CMC)
Roberts North 102, CMCThe Kauffman bracket skein algebra of a surface is at once related to quantum topology and to hyperbolic geometry. In this talk, we consider a generalization of the skein algebra […]
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Using quantum statistical mechanical systems to study real quadratic fields (Jane Panangaden, Pitzer College)
Estella 2099The original Bost-Connes system was constructed in 1990 and is a QSM system with deep connections to the field of rationals. In particular, its partition function is the Riemann-zeta function […]
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Quiver categorification of quandle invariants (Sam Nelson, CMC)
Estella 2099Quiver structures are naturally associated to subsets of the endomorphism sets of quandles and other knot-coloring structures, providing a natural form of categorification of homset invariants and their enhancements. In […]
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Point-counting and topology of algebraic varieties (Siddarth Kannan, UCLA)
Estella 2099A projective algebraic variety X is the zero locus of a collection of homogeneous polynomials, in projective space. When the polynomials have integer coefficients, we can think of the k-valued […]
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The restricted variable Kakeya problem (Pete Clark, University of Georgia)
Estella 2099For a finite field F_q, a subset of F_q^N is a Kakeya set if it contains a line in every direction (i.e., a coset of every one-dimensional linear subspace). The finite […]
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Homological mirror symmetry, curve counting, and a classical example: 27 lines on a nonsingular cubic surface (Reggie Anderson, CMC)
Estella 2099Though mirror symmetry requires much technical background, it gained traction in the mathematical community when physicists Candelas-de la Ossa-Green-Parkes discovered enumerative invariants counting the number of rational degree d curves […]
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Almost-prime times in horospherical flows (Taylor McAdam, Pomona)
Estella 2099There is a rich connection between homogeneous dynamics and number theory. Often in such applications it is desirable for dynamical results to be effective (i.e. the rates of convergence for […]
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Sublattices and subrings of Z^n and random finite abelian groups (Nathan Kaplan, UC Irvine)
Estella 2099How many sublattices of Zn have index at most X? If we choose such a lattice L at random, what is the probability that Zn/L is cyclic? What is the probability that its […]
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Well-rounded lattices and security: what we (don’t) know (Camilla Hollanti, Aalto University, Finland)
Estella 2099I will give a brief introduction to well-rounded lattices and to their utility in wireless communications and post-quantum security. We will see how the lattice theta series naturally arises in […]